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A new iterative algorithm for the multiple-sets split feasibility problem and the split equality fixed point problem. (English) Zbl 1481.47089

Summary: In this paper, we propose a new iterative algorithm for solving the multiple-sets split feasibility problem and the split equality fixed point problem of firmly quasi-nonexpansive mappings in real Hilbert spaces. Under very mild conditions, we prove a weak convergence theorem for our algorithm using projection method and the properties of firmly quasi-nonexpansive mappings. Our result improves and extends the corresponding ones announced by some others in the earlier and recent literature.

MSC:

47J25 Iterative procedures involving nonlinear operators
49J53 Set-valued and variational analysis
49M37 Numerical methods based on nonlinear programming
90C25 Convex programming
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